On effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914636377358336 |
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| author | Wolff, Markus |
| author_facet | Wolff, Markus |
| contents | We study the effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes, both in the spacelike and the timelike case, respectively. In the spacelike case, we study totally umbilic warped product graphs and give a full characterization of embedded surfaces with constant spacetime mean curvature using an Alexandrov Theorem by Brendle and Borghini--Fogagnolo--Pinamonti. In the timelike case, we achieve a characterization of photon surfaces with constant umbilicity factor similar to a result by Cederbaum--Galloway. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11229 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes Wolff, Markus Differential Geometry 53C24 (Primary) 53C21, 83C20 (Secondary) We study the effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes, both in the spacelike and the timelike case, respectively. In the spacelike case, we study totally umbilic warped product graphs and give a full characterization of embedded surfaces with constant spacetime mean curvature using an Alexandrov Theorem by Brendle and Borghini--Fogagnolo--Pinamonti. In the timelike case, we achieve a characterization of photon surfaces with constant umbilicity factor similar to a result by Cederbaum--Galloway. |
| title | On effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes |
| topic | Differential Geometry 53C24 (Primary) 53C21, 83C20 (Secondary) |
| url | https://arxiv.org/abs/2310.11229 |